Question

Two cars are moving is the same direction with a speed of $30{\text{km h}}^{-1}$. They are separated from each other by $5\text{km}$. Third car moving in the opposite direction meets the two cars after an interval of 4 minutes. What is the speed of the third car?

• A. $30{\text{km h}}^{-1}$
• B. $35{\text{km h}}^{-1}$
• C. $40{\text{km h}}^{-1}$
• D. $45{\text{km h}}^{-1}$

Answer 1

The correct option is D $45{\text{km h}}^{-1}$

Suppose the first car is moving ahead of second car by $5\text{km}$
Let the speed of the third car be $x$
Relative distance between first car and second car $=5\text{km}$
Relative speed of third car w.r.t second car $=(x+30)\text{km/h}$ ($\because$ second car is moving in opposite direction to that of third car)
Relative distance $=\text{relative speed}\times \text{time}$
$\Rightarrow 5=(x+30)\times \left(\frac{4}{60}\right)$
$\therefore x=45\text{km/h}$